MGMT 675
AI-Assisted Financial Analysis

Autoregression
Overview
- We want to forecast a time series.
- returns, interest rates, oil price, cash flows, …
- Possible models:
- ARIMA (autoregressive integrated moving average)
- exponential smoothing
- neural networks
- We’ll do AR models.
Autocorrelations
- Autocorrelation = correlation of a variable with its lagged value
- First-order autocorrelation \(=\text{corr}(x_t, x_{t+1})\)
- \(p\)–th order autocorrelation \(=\text{corr}(x_t, x_{t+p})\)
- E.g., \(p=12\) in monthly data or \(p=4\) in quarterly data because of seasonality
Autocorrelation of HML
- Ask Julius to use pandas-datareader to download the monthly Fama-French factors from Ken French’s data library.
- Ask Julius to produce a plot of the autocorrelation function (acf) for HML.
Autoregressions
- An autoregression is a regression of a variable on its own lags: \[x_t = \alpha + \beta_1x_{t-1} + \cdots + \beta_px_{t-p} + \varepsilon_t\]
- Ask Julius to fit an AR(1) for HML.
- Ask Julius to use the AR(1) model to forecast HML for the next 12 months and to plot the last 2 years and the forecasts.
More examples
Ask Julius to plot the ACF, fit an AR model, and forecast the following:
Percent change in crude price: Ask Julius to use pandas-datareader to download crude oil prices starting in 1980 from FRED, to downsample to end-of-month, and to compute percent changes.
Change in Treasury yields: Ask Julius to use pandas-datareader to download 10-year Treasury yields starting in 1980 from FRED, to downsample to monthly, and to compute changes.
Vector Autoregression
- Forecast related variables based on their mutual lags
- Example: does this month’s SMB return forecast next month’s HML return?
- Ask Julius to run a VAR(1) on the Fama-French factors and provide a summary of the results.